Monte Carlo simulation of φ⁴₂ and O(N)φ⁴₃ theories

We report lattice simulations of $\phi^4_2$ and $O(N)\,\phi^4$ models, performed by means of a Monte Carlo method based on the all-order strong coupling expansion (worm algorithm). The investigation of the non-perturbative features of the $\phi^4$ continuum limit in two dimensions lead us to the result $g/\mu^2 = 11.15 \pm 0.06_{stat} \pm 0.03_{syst}$ for the critical coupling. Furthermore we present preliminary results for the three-dimensional $O(2)\phi^4\,$ model using the worm algorithm with the extention to $O(N)\phi^4\,$ in $D$ dimensions.